Quid est quod?

Omnipotence is from the beginnings of monotheism, an incommunicable attribute of God, usually accompanied by other attributes – Omniscience and Omnipresence.

This divine quality would be the possibility of having in itself the ability to do all things. The main religions whose God is omnipotent are the Abrahamic religions.

Since the advent of classical atheism, several paradoxes have been developed, pointing to the presence of logical inconsistencies – contradictions – in this attribute, many of them concluding that it is impossible for real omnipotence to exist. The best known of such is the paradox of stone.

From this point of view, various aspects have emerged in the attempt to invalidate such paradoxes or point out other definitions for omnipotence, the main and most defended of these views being the scholastic side presented by Thomas Aquinas in his compiled Summa Theologiæ.

Next, I'll go into a little more detail on each side.

Thomas Aquinas: The Scholastic Current

Thomas Aquinas (1225-1274)

The scholastic omnipotence is "logical" omnipotence, which is most defended in theology. One of his most notable supporters was the friar, philosopher and theologian Thomas Aquinas, considered one of the fathers of the Catholic church and one of the greatest theologians of all time. Thomas Aquinas is known for his gigantic work Summa Theologiæ, in which he made various objections to God, and answered all of them.

Considering also the classical view of omnipotence, they argues that God could accomplish only what is logically possible, thus not violating the principles of classical logic. Proponents of this position argue that just as contradictions can never be part of reality, they can not be considered entities - they are literally nothing. As nothing is the absence of being, the everything has nothing included and therefore being able to do "everything" does not include the realization of contradictions. The concern of the scholastics, before classifying power, is to make sense.

Thomas Aquinas affirms that God's omnipotence is based on the realization of acts in the absolute possible, but this does not include absolute impossibility.

The absolute possible is not so called in reference either to higher causes, or to inferior causes, but in reference to itself. But the possible in reference to some power is named possible in reference to its proximate cause. Hence those things which it belongs to God alone to do immediately--as, for example, to create, to justify, and the like--are said to be possible in reference to a higher cause. Those things, however, which are of such kind as to be done by inferior causes are said to be possible in reference to those inferior causes. For it is according to the condition of the proximate cause that the effect has contingency or necessity, as was shown above (I:14:1 ad 2). Thus is it that the wisdom of the world is deemed foolish, because what is impossible to nature, it judges to be impossible to God. So it is clear that the omnipotence of God does not take away from things their impossibility and necessity.

First of all, Aquinas here didn't refer to the possible and impossible in the common sense, but to the metaphysical possible and impossible. It is impossible for us to practice levitation, for example, but it is not to that kind of impossible that Aquinas refers, for this kind of possibility is not a logical impossibility. The reference is to beings who don't fit into any possible world, such as a triangle whose hypotenuse is greater than the sum of the legs, or anything that violates the principles of classical logic such as noncontradiction. I recommend that you read about the Possible World concept, proposed by Gottfried Leibniz.

Thomas also explained about this:

All confess that God is omnipotent; but it seems difficult to explain in what His omnipotence precisely consists: for there may be doubt as to the precise meaning of the word 'all' when we say that God can do all things. If, however, we consider the matter aright, since power is said in reference to possible things, this phrase, "God can do all things," is rightly understood to mean that God can do all things that are possible; and for this reason He is said to be omnipotent. Now according to the Philosopher (Metaph. v, 17), a thing is said to be possible in two ways.

First in relation to some power, thus whatever is subject to human power is said to be possible to man.

Secondly absolutely, on account of the relation in which the very terms stand to each other. Now God cannot be said to be omnipotent through being able to do all things that are possible to created nature; for the divine power extends farther than that. If, however, we were to say that God is omnipotent because He can do all things that are possible to His power, there would be a vicious circle in explaining the nature of His power. For this would be saying nothing else but that God is omnipotent, because He can do all that He is able to do.

In other words, it would be possible for God to do anything, including the humanly impossible, as I had previously said. However, the logical impossible can not be put into power, and consequently can not be done, as St. Thomas explains shortly.

It remains therefore, that God is called omnipotent because He can do all things that are possible absolutely; which is the second way of saying a thing is possible. For a thing is said to be possible or impossible absolutely, according to the relation in which the very terms stand to one another, possible if the predicate is not incompatible with the subject, as that Socrates sits; and absolutely impossible when the predicate is altogether incompatible with the subject, as, for instance, that a man is a donkey.

It must, however, be remembered that since every agent produces an effect like itself, to each active power there corresponds a thing possible as its proper object according to the nature of that act on which its active power is founded; for instance, the power of giving warmth is related as to its proper object to the being capable of being warmed. The divine existence, however, upon which the nature of power in God is founded, is infinite, and is not limited to any genus of being; but possesses within itself the perfection of all being. Whence, whatsoever has or can have the nature of being, is numbered among the absolutely possible things, in respect of which God is called omnipotent. Now nothing is opposed to the idea of being except non-being. Therefore, that which implies being and non-being at the same time is repugnant to the idea of an absolutely possible thing, within the scope of the divine omnipotence. For such cannot come under the divine omnipotence, not because of any defect in the power of God, but because it has not the nature of a feasible or possible thing. Therefore, everything that does not imply a contradiction in terms, is numbered amongst those possible things, in respect of which God is called omnipotent: whereas whatever implies contradiction does not come within the scope of divine omnipotence, because it cannot have the aspect of possibility. Hence it is better to say that such things cannot be done, than that God cannot do them. Nor is this contrary to the word of the angel, saying: "No word shall be impossible with God." For whatever implies a contradiction cannot be a word, because no intellect can possibly conceive such a thing.

As a bonus, the writer Clive Staples Lewis also wrote about omnipotence. C. S. Lewis is best known for his work The Chronicles of Narnia. In his book The Problem os Pain he took a vision similar to that of Thomas Aquinas about the divine omnipotence.

His Omnipotence means power to do all that is intrinsically possible, not to do the intrinsically impossible. You may attribute miracles to him, but not nonsense. This is no limit to his power. If you choose to say 'God can give a creature free will and at the same time withhold free will from it,' you have not succeeded in saying anything about God: meaningless combinations of words do not suddenly acquire meaning simply because we prefix to them the two other words 'God can.'... It is no more possible for God than for the weakest of his creatures to carry out both of two mutually exclusive alternatives; not because his power meets an obstacle, but because nonsense remains nonsense even when we talk it about God.

You may think that if the omnipotent is restricted or conditioned to something external to it, it invalidates its omnipotence. In fact, this makes sense from the semantics of the word. However, it should be remembered that the point is that nothing external to the omnipotent can constrain it, so that the only thing as great as it, is itself. In this line of reasoning, many scholastic philosophers believe that God must be the very set of necessary laws that governs existence, for they are above all else. The philosopher William L. Craig defends that the fundamental principles of logic and mathematics are representations of the way God reasoned. I.e., they are not external laws to God to which he is conditioned, or abstract objects that limit God, but rather that they are aspects of the mind of God.[4]

Despite having several advocates over the years, there is neither a principal representative of this point of view, nor so many advocates as scholasticism. The illogical view of omnipotence preaches that God could violate even the laws of classical logic, such as the law of noncontradiction the law of excluded middle, and the law of identity, and make mathematical absurdities like a triangle whose hypotenuse is greater than the sum of the legs.

Nicholas of Cusa (1401-1464)

The main defense to universal possibilism probably comes from René Descartes, expressed in his Meditations on First Philosophy. Among them, it would include the very creation of logical and mathematical truths, like the classical laws of thought.[5] In spite of his defense, Descartes' universal possibilism is considered absurd and unsustainable, as is the idea of absolute relativism, for he demands the negation of himself for his own affirmation, as W. L. Craig explains.[4]

St. Pier Damiani in De divina omnipotentia accused St. Girolamus of being blasphemous, for claiming that God could not undo what was done, i.e., accuse the past. For St. Pier Damiani, figures like St. Girolamus and Thomas Aquinas were blaspheming in trying to limitate God.

Cardinal Nicholas of Cusa in De douta ignorantia argued that God, being infinite, is coincidentia oppositorum. I.e., should have all existing properties, and between these properties should have properties of both being and non-being, both positive and negative. This logically encompasses properties that contradict each other. In this way, it would be possible for God not only to be contradictory, but also to create contradictory objects.

Since I am going to discuss the maximum learning of ignorance, I must deal with the nature of Maximality. Now, I give the name “Maximum” to that than which there cannot be anything greater. But fullness befits what is one. Thus, oneness—which is also being—coincides with Maximality. But if such oneness is altogether free from all relation and contraction, obviously nothing is opposed to it, since it is Absolute Maximality. Thus, the Maximum is the Absolute One which is all things. And all things are in the Maximum (for it is the Maximum); and since nothing is opposed to it, the Minimum likewise coincides with it, and hence the Maximum is also in all things. And because it is absolute, it is, actually, every possible being; it contracts nothing from things, all of which [derive] from it. In the first book I shall strive to investigate incomprehensibly above human reason-this Maximum, which the faith of all nations indubitably believes to be God. [I shall investigate] with the guidance of Him “who alone dwells in inaccessible light.”

Think of omnipotence as the possibility of performing all acts that can be expressed by words that assume consistent meaning in potency, and to carry them out, it is enough for that power in act. This could explain some paradoxes such as the paradox of stone, so that God has in himself both the act of creating the stone and the act of lift it.

In addition, there are two current philosophical currents that can support the anti-scholastic view of omnipotence. These are paraconsistent logic and dialaletheism.

Paraconsistent logic is a non-classical logic that accepts and treats contradictions (DA SILVA FILHO, 1999), a logic is paraconsistent if its logical consequence relation (⊨, either semantic or proof theoretic) is not explosive (PRIEST et al, 2016). Dialetheism is the view that there are dialetheias. One can define a contradiction as a couple of sentences, one of which is the negation of the other, or as a conjunction of such sentences. (PRIEST 2017).[7]

Recently, limitations were seen in classical logic and in Aristotelian principles such as non-contradiction, which encouraged mathematicians to base paraconsistent logic, which deals with the explosiveness of contradictions, and dialetheism, which accepts that there are real contradictions. An example of such applications are the paradoxes of self-reference, such as the Liar paradox, which consists of the following:

$ (1) $ Proposition $ (1) $ is false.

Or:

$ (a) $ Proposition $ (b) $ is true.

$ (b) $ Proposition $ (a) $ is false.

This paradox forces us to assume that an affirmation can be both true and false, which clearly violates the law of non-contradiction. This demonstrates a linguistic limitation on the principle of non-contradiction. A argument used is that if linguistics, which is a human faculty, can violate the non-contradiction law, why omnipotence, which is a transcendent quality, couldn't also violate this law?

Another example is Russell's paradox, highlighting the Barber's paradox, which derives from it.

$ M=\{A\mid A\not\in A\} $

Think of a situation where a city has only one barber, and men only have two ways to shave, 1) shaving alone or 2) going to the barber. This barber, however, does not shave anyone who shaves alone, and shaves all those who do not shave alone. If so, who shaves the barber? Because 1) if the barber shaves, it means he shaves himself, and therefore, he is not among the people he shaves; 2) if the barber doesn't shave alone, it means he's on the list of people he shaves.

Jean-Yves Beziau and Newton da Costa spoke about this in the 1st World Congress on Logic and Religion. In their words:

We say that an object is paraconsistent iff it has both a property P and the negation #P of this property, # being a paraconsistent negation, that is to say an operator not obeying the principle of explosion (from P and #P, everything follows) but having enough properties to be considered as a negation. We are considering here "object" in a very general and abstract sense: any kind of thing or being. A quanton can be considered as a paraconsistent object being both a particle and a non particle (a wave). We defend here that God is a paraconsistent object, having many paraconsistent properties.

Another point is that this doesn't just apply to linguistics. Paraconsistent logic is also used in computing and artificial intelligence.

We may also notice situations in quantum physics where the principle of noncontradiction is violated, as is the case with the hypothetical experiment of Erwin Schrödinger's cat, that as long as there is no observer, the cat is simultaneously alive and dead. Note also the paraconsistency in the wave-particle duality, in which a quantum can behave as both wave and particle.

Dialetheism, however, does not accept that all contradictions are true, and therefore must be distinguished from trivialism. And already mentioned philosophers such as St. Pier Damiani and Nicholas of Cusa were considered by Graham Priest as having taken positions close to the current dialetheism.[7]

In conclusion, there is enough philosophical and logical basis to assume that omnipotence may violate the principle of non-contradiction. For that, it would suffice that she was paraconsistent. Since paraconsistency is an area of logic, we can not even say that it is illogical, since logic in its entirety encompasses much more possibilities than the classical laws of thought, and of classical and Aristotelian logic.

Paradoxes: Frequent questions

First of all, to be considered, the question must assume consistent meaning. That is, if the question absolutely does not make sense, it can not even be considered a question. A nonsense is a nonsense, no matter if it has the word "omnipotence" in between.

Knowing the point of view, the solution to it is practically obvious, so I don't need to point out how each current responds to them. Therefore, this part will be more about what I think about it.

Could an omnipotent being create a stone he can not even lift?

Short answer: Yes.

As I said earlier, think of omnipotence as “the possibility of performing all acts that can be expressed by words that assume consistent meaning”. Accepting that omnipotence has all the properties that can be had, and that this would include properties that are opposed to each other, it would be possible, therefore, to have both the property of impotence and the property of power, i.e., for that, it would suffice to have both the act of creating the stone, and the act of lifting it.

I'll give an example of a similar set to omnipotence, which may help to better understand the point.

In math, the set of integers $ \mathbb{Z} $ encompasses both positive numbers and negative numbers. Among these numbers, there are those that completely oppose each other (for example, in the set of integers have both $ -5 $ and $ 5 $, even one being completely opposite to the other). The main point is that in an infinite set, there is the possibility that there are properties within it that counteract one another. Omnipotence, as an infinite set, must function in the same way, having one property (the act of creating the stone that can not be lifted) that opposes the other (the act of lifting the stone).

In this way, one of the possible resolutions to the paradox lies in the coincidentia oppositorum itself. The fact that omnipotence is an infinite set of acts in potency makes it possible for it to have acts that oppose each other while having the power to raise the stone and the power to lift it.

In addition, as a matter of curiosity, there is a concept proposed by the mathematician Georg Cantor called "Absolute Infinity", which would be an absolutely unlimited set that transcends all transfinites and has all sets within it. This concept is often associated with God.

Could an omnipotent being create another omnipotent being?

Here is a problem that even the fact of having infinite properties can't solve.

Short answer: Yes, and no.

Nevertheless, what makes him an omnipotent being is the properties he possesses. An omnipotent one is not a contingent entity like us, of which there can be similar billion, it is a being that, if it possesses these characteristics, is classifiable as.

As an infinite set that transcends and encompasses all possible properties, there can be nothing external that opposes an omnipotent. In other words, he can create a being with the same properties as he, but from the point that this being has the same properties as it, that being would be nothing more than himself. This can be placed as part of a philosophical principle known as the "Law of Identity".

Could an omnipotent renounce his omnipotence?

Short answer: Yes.

At this point, I need to get into Christian theology a bit. In Christianity, Jesus is considered God (John 1:1), and became man (John 1:14), emptied of himself (Philippians 2:5-7).

We can say that, from the point where he became man and emptied himself, he was renouncing his attributes.

And in the same way, the same omnipotent can be omnipotent again, as it also happened later.

Note: This comment is not doing any proselytism. I use Christianity as the basis because — at least in the West where I live — it is the main monotheistic religion.

Note: Some Christian denominations disagree with the doctrine of the Holy Trinity.

Could an omnipotent kill himself?

Short answer: Yes.

The same point used for the stone paradox can be used for the death of an omnipotent.

An omnipotent, as having all the characteristics united together, must have between these characteristics, both "death" and "life".

In this way, even though he might be dead, he could live, and even though he was alive, he might be dead.

What would happen in a fight between two omnipotent?

Short answer: Absurd.

The idea of the existence of more than one omnipotent being is the incarnation of incoherence and the manifestation of ignorance. You'll see just such nonsense in works like Suggsverse.

↑DESCARTES, René. Meditations on First Philosophy, trans. John Cottingham, Robert Stoothoff, and Dugald Murdoch, in The Philosophical Writings of Descartes (Volume 2). Cambridge University Press, 1984.